JP2009204823A - Simulation method and program for simulation - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To enable measuring an intensity distribution of light radiated to a substrate surface through a mask in a short time similarly to a thin film mask approximation calculation and more accurately measured than the thin film mask approximation calculation. <P>SOLUTION: The simulation method to be used for manufacturing a semiconductor device includes the following steps. A virtual mask is set (S52), the mask having no thickness but having a transmittance and a phase distribution, in which a transmissive part where propagation of light is not inhibited by a side face of a shielding part due to a three-dimensional structure is regarded as a new opening, when the mask is viewed from a point light source of oblique illumination; a phase difference is set (S54) between the zero-order diffracted light and the first-order diffracted light, which are determined, with respect to the diffracted light on a pupil plane in a projection optical system when the virtual mask is used, by the relationship depending on the distance between the zero-order diffracted light and the first-order diffracted light on the pupil plane, the thickness of the shielding part, the angle between the incident light from the light source to the mask and the optical axis; and the intensity of light on the substrate surface where the pattern of the mask is transferred is simulated (S55) based on the set virtual mask and the phase difference. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a lithography simulation technique used for manufacturing a semiconductor device, and more particularly to a simulation method for simulating light intensity on a substrate in designing a lithography process. Furthermore, the present invention relates to a program for executing this simulation method by a computer.

  In the manufacture of a 45 nm node semiconductor device, when a lithography process using ArF light immersion and high NA is used, the size of the pattern on the mask is almost the same as the wavelength of ArF light. In this case, the waveguide effect by mask topography and the influence of shielding by oblique incident light cannot be ignored.

  Therefore, in lithography simulation for LSI design, for example, when simulating the intensity distribution of light irradiated onto the substrate surface through the mask, the thickness of the mask and the incident angle of light must be strictly considered. Don't be. That is, exact solution calculation of Maxwell's equations considering the mask three-dimensional structure is essential. However, in this case, it takes time on the order of 10 times to 100 times that of the simulation (thin film mask approximate calculation) performed with the conventional mask without thickness. In actual development, the speed of design is important, and such an increase in calculation time is a serious problem.

  In order to avoid this problem, the size of the translucent part and the transparent part when a three-dimensional mask pattern is expected from the light source is geometrically taken into consideration, and the plane mask pattern (thin film mask) is newly redefined. A method has been proposed in which an optical image that is almost the same as the strict consideration calculation is obtained in a short time (see, for example, Patent Document 1). However, in this type of method, the phase difference of the semi-transmissive part in the thin film mask approximate calculation is constant regardless of the incident angle of the illumination light, and there is a possibility that the prediction accuracy of the focus shift is low.

As described above, in the light intensity distribution simulation method for measuring the intensity distribution of light irradiated on the substrate surface through the mask, accurate measurement is possible with the exact solution calculation of the Maxwell equation considering the mask three-dimensional structure. There was a problem that enormous calculation time was required. On the other hand, as in Patent Document 1, in the thin film mask approximate calculation in which a three-dimensional mask pattern is newly redefined as a planar mask pattern, the calculation time can be shortened, but accurate measurement cannot be performed due to the influence of the semi-transmissive portion. was there.
JP 2007-273560 A

  In the lithography simulation, the present invention can measure the intensity distribution of light irradiated on the substrate surface through the mask in a short time as in the thin film mask approximate calculation, and more accurately than the thin film mask approximate calculation. It is an object of the present invention to provide a simulation method capable of performing the above.

  A simulation method according to an aspect of the present invention is a simulation method in which illumination light is obliquely applied to a mask plane, and a pattern formed on the mask is transferred onto a substrate via a projection optical system. The distance between the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system, the thickness of the shielding part formed on the mask, the optical axis direction of the irradiation light and the incident direction on the mask The zero-order diffracted light and the first order determined in accordance with at least one of a specified angle and a difference amount between the mask pattern size and the half-cycle size of the mask pattern when the mask pattern is a periodic pattern. The method includes a step of setting a phase difference with the folded light, and a step of executing a simulation based on the set phase difference.

  A program according to an aspect of the present invention is for executing a simulation of irradiating illumination light obliquely on a mask plane and transferring a pattern formed on the mask onto a substrate via a projection optical system. A distance between 0th-order diffracted light and 1st-order diffracted light on the pupil plane of the projection optical system, a thickness of a shielding portion formed on the mask, an optical axis direction of the irradiation light, and the mask The next time determined in accordance with an angle defined by the incident direction and at least one of a difference amount between the mask pattern size and the half cycle size of the mask pattern when the mask pattern is a periodic pattern. Causing the computer to execute means for setting a phase difference between the folded light and the first-order diffracted light, and means for executing a simulation based on the set phase difference. And Features

  According to the present invention, the intensity distribution of light irradiated on the substrate surface through the mask can be measured in a short time as in the thin film mask approximate calculation, and more accurately than the thin film mask approximate calculation. it can.

  Before describing the embodiments of the invention, the basic principle of the present invention will be described.

FIG. 1 is a schematic block diagram showing an example of a projection exposure apparatus used in the present invention. 11 is a light source, 12 is a mask, 13 is a projection optical system, and 14 is a wafer (substrate). This example is an oblique illumination method using second illumination as the light source 11. For this reason, the light from the light source 11 (point light source A) is irradiated obliquely with respect to the mask plane, and the 0th-order diffracted light and the 1st-order diffracted light from the mask 12 are converged by the projection optical system 13 and connected to the wafer 14. It has come to be imaged. Here, the positions of the zero-order diffracted light and the first-order diffracted light on the pupil plane of the projection optical system 13 are separated by a distance corresponding to the pattern pitch on the mask, and the distance x is HP, If the wavelength of the exposure light is λ, x = λ / (2 · HP)
It is represented by

  When such a projection exposure apparatus is used, the light intensity distribution on the wafer 14 is obtained by simulation. A desired pattern can be formed on the wafer 14 by correcting the pattern of the mask 12 based on the simulation result.

  As described above, the calculation considering the mask three-dimensional structure can be measured accurately but takes a lot of time. Therefore, as in (Patent Document 1), a thin film mask definition using a shadow model has been studied.

  First, as shown in FIG. 2, a mask 21 having a three-dimensional structure is newly defined as a planar mask 31 in consideration of only a shadow effect due to oblique incidence. In the figure, θ is the incident angle of the exposure light (angle formed by the optical axis direction of the irradiated light and the incident direction of the irradiated light on the mask), and d is the thickness of the light shielding portion (including the translucent portion) 22. is there.

  For example, in order to resolve a 1: 1 contact hole pattern with a pitch of 100 nm, the illumination condition is 1.3 NA, the fourth illumination, the distance σ = 0.8 from the optical axis to the center of the fourth illumination eye, the exposure Assuming that the reduction ratio of the apparatus is Mag = 4, the light incident angle from the point light source at the center of each eye of the fourth illumination to the mask is determined as follows.

sinθ = NA × σ / Mag = 0.26 ∴θ = 15.07deg
For simplification, it is assumed that the portion 32 which is shaded by light irradiation from a direction inclined by θ from the optical axis cannot transmit illumination light.

The newly set size w ′ of the opening (mask pattern) is tan θ = 0.269260 when the size w of the original opening of the mask pattern is 70 nm.
w ′ = w−d · tan θ = 65.29 nm
It becomes.

  Here, in order to consider the phase difference in the shadow portion 32 around the opening, as shown in FIG. 3, calculation is performed by giving a certain transmittance / phase to the shadow portion 32 (fringe). A method has been proposed. However, in such mask calculation, the phase distribution of the diffracted light transmitted through the fringe 32 is uniquely determined.

  FIG. 4 shows the half-pitch (HP) dependence of the phase difference between the 0th-order diffracted light and the 1st-order diffracted light with a 1: 1 periodic pattern. From this figure, it can be seen that as HP increases, the phase difference between the 0th order diffracted light and the 1st order diffracted light becomes smaller.

  The phase difference of the diffracted light greatly affects the simulation accuracy.

  Therefore, the conventional method is insufficient, and it is necessary to correctly incorporate the effect of the phase difference distribution between the diffracted lights in order to perform accurate simulation. In consideration of this point, the phase in the fringe is not fixed, but the phase difference distribution between diffracted lights according to various parameters is considered.

FIG. 5 is a schematic diagram showing the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system. The diffracted light is represented by an arrow, the magnitude of the arrow represents the amplitude of the diffracted light, and the angle formed by the arrow with the light source direction of the optical axis being positive represents the phase. The three first-order diffracted lights indicate that diffracted lights appear at different positions when patterns having different HPs HP1, HP2, and HP3 are illuminated from a point light source on the optical axis. Here, the relationship of each HP is HP1 <HP2 <HP3. From FIG. 4, the smaller the HP is, the larger the phase difference between the 0th order diffracted light and the 1st order diffracted light. Further, the distances x1, x2, and x3 between the 0th-order diffracted light and the 1st-order diffracted light corresponding to each pattern are x = λ / (2 · HP)
Accordingly, the relationship of x1>x2> x3 is established.

  Therefore, it is possible to give the phase difference Δφ as a variable having the 0th-order diffracted light-1st-order diffracted light interval x on the pupil plane as a variable.

FIG. 6 is a diagram showing the 0th-first order phase difference Δφ at the position on the pupil plane. The phase difference Δφ is
Δφ = f (x, bias, θinc, d)
x: Distance between 0th-order diffracted light and 1st-order diffracted light on the pupil plane
bias: difference amount between the pattern size of the periodic mask pattern and HP θinc: incident angle of illumination light d: expressed as the film thickness of the mask shielding part, and takes different values depending on the difference of bias, θinc, d. Each graph is different. It takes a lot of time to calculate different phase differences depending on these conditions, and calculating at the time of simulation causes a reduction in the speed of the simulation.

  Therefore, the phase difference under various lithography conditions is calculated in advance, and the result is stored in the DB or converted into a function. At this time, the absolute value of the phase difference may be stored or functioned, or the difference between the phase of the mask three-dimensional structure consideration calculation (exact calculation) and the phase of the thin film mask approximation calculation may be stored. At the time of simulation, a necessary phase difference is extracted from the DB and used.

  Also, instead of performing the first exact calculation under all conditions, when it is an intermediate condition of a combination of two adjacent conditions that already exist in the DB, a phase difference obtained by interpolating them is used. Alternatively, a function model is created from conditions that already exist in the DB, and the phase difference is calculated based on the function model.

Furthermore, in the simulation, the phase of the diffracted light by the thin film mask approximate calculation is input by the following method.
・ Input aberrations in the simulation as aberrations in the pupil.

-Input into the phase term of direct diffracted light (replaces the result of Fourier transform (equivalent to distribution on the pupil) during thin film mask approximation calculation)
By using such a method, the approximate calculation considering the mask three-dimensional structure can be performed at the same speed as the approximate calculation of the thin film mask. Hereinafter, an embodiment of the present invention to which the above idea is applied will be described with reference to the drawings.

(Embodiment)
In the design of a lithography process in the manufacture of a semiconductor device, the corresponding contact on the mask so that the contact hole pattern 41 as shown in FIG. 7 can be transferred within a desired dimension onto the wafer substrate coated with a photosensitive film. An example of hole pattern dimension design is shown.

  It was assumed that the exposure apparatus having the configuration shown in FIG. 1 was used and a light source 42 capable of fourth illumination was used as shown in FIG. The distance from the optical axis to the center of the eye is σ = 0.85, the size of each eye is σ = 0.05, and the mask magnification of the projection exposure apparatus is 4.

  The pitch of the contact holes 41 was 200 nm, and the opening size was 70 nm □. The dimensions are shown as numerical values converted on the wafer.

  FIG. 9 is a flowchart for explaining the operation of the optical image calculation unit in the present embodiment.

  First, illumination conditions, mask conditions, pattern types, pattern pitches, pattern dimensions, light incident angles, and the like as described above were set as initial values (step S51).

  Next, consider the transfer characteristics when forming an image of a 1: 3 contact hole provided on an attenuated phase shift mask (Attenuated phase shift mask) on a wafer substrate coated with a photosensitive film using an ArF immersion exposure apparatus. Therefore, the optical image calculation was performed according to the following procedure.

At this time, the light incident angle θ from the second illumination shown in FIG. 8 arranged in the x direction of FIG.
sinθ = NA × σ / Mag
∴θ = 16.04deg
Therefore, of the incident light that falls within the size w = 70 nm of the opening, the region that is not reflected by the shielding part is
w ′ = wd · tan θ = 65.0 nm
It is.

  Therefore, a 65.0 nm × 70 nm opening is defined as a new opening with respect to the second illumination light, and a plane mask is defined with a shift of the center of gravity position of the pattern assumed from the expected angle (step). S52), the diffracted light distribution on the pupil was calculated (step S53). At this time, the phase of the diffracted light is constant regardless of the angle of oblique incidence because it is calculated as a planar mask, although it actually has an angle dependency of oblique incidence.

  Subsequently, the phase difference between the 0th-order diffracted light and the 1st-order diffracted light obtained by performing rigorous calculation using the three-dimensional consideration mask is called from the DB (step S54). Here, the phase difference called from the DB is obtained by performing a strict calculation using a three-dimensional consideration mask under necessary conditions in advance and storing the pattern type, pattern pitch, pattern bias, and incident angle of illumination light in the DB as parameters. is there.

  Next, based on the phase of the 0th order diffracted light on the pupil obtained by the thin film mask calculation and the phase difference called from the DB, the phase of the first order diffracted light is newly calculated, and the phase of the first order diffracted light by the thin film mask calculation is calculated. (Step S55). Next, the 0th-order diffracted light and the 1st-order diffracted light are subjected to inverse Fourier transform, and output as a light intensity distribution simulation result in the photosensitive film on the wafer substrate (step S56). In the present embodiment, since the fourth illumination is used, the light intensity distribution by the second illumination shown in FIG. 8 arranged in the y direction in FIG. 7 is also output in the same manner, and the results of both are combined. A final light intensity distribution was obtained. Thus, the contact hole pattern dimensions obtained when the image was formed were obtained.

  As described above, according to the present embodiment, the same calculation as the thin film mask approximate calculation is performed, and the phase difference of the semi-transmissive portion is changed according to the incident angle, so that the light irradiated on the substrate surface through the mask can be changed. The intensity distribution can be measured in a short time similarly to the thin film mask approximate calculation and can be measured more accurately than the thin film mask approximate calculation.

  Next, processing such as adjusting the bias of the mask such as OPC is performed so that the contact hole can be transferred within a desired size range, and then the above procedure is repeated to design the contact hole size on the corresponding mask. .

  The flowchart at this time is shown in FIG. First, a mask finished dimension allowable range, illumination conditions, etc. are initialized (step S61), and an initial mask dimension is set accordingly (step S62). Next, an optical image is calculated by simulation based on the flowchart shown in FIG. 9 (step S63). Then, it is determined whether or not the pattern dimension predicted from the optical image is within a desired dimension range (step S64). If the predicted pattern dimension is outside the range of the desired dimension, the mask dimension is changed (step S65), and the process returns to S63 to perform another calculation. If the predicted pattern dimension is within the range of the desired dimension, the mask dimension at this time is fixed as a design value (step S66).

The mask produced using the contact hole pattern design value on the mask obtained by the above procedure was imaged in the photosensitive film on the wafer substrate using the projection exposure apparatus, and the photosensitive film on the wafer was developed. As a result, a resist pattern as desired was obtained. At this time, the simulation time for pattern design can be reduced to about 1/10 ² compared to the calculation that strictly considers the angle of the oblique incident light and the mask three-dimensional structure, and the oblique incident light. A design with the same accuracy as the angle and mask steric structure was considered.

  FIG. 11 is a diagram showing an optical image calculation result in the present embodiment in comparison with a strict calculation result. The solid line is the exact calculation, and the broken line is the thin film mask approximate calculation according to the present embodiment. From this figure, it can be seen that the approximate calculation according to the present embodiment exactly agrees with the calculation result in consideration of the angle of oblique incident light and the mask three-dimensional structure.

  As described above, according to the present embodiment, it is possible to perform a high-speed light intensity distribution simulation that incorporates the oblique incidence of exposure light and the three-dimensional mask effect without performing exact calculation of the three-dimensional mask structure each time. Further, by using the calculation result stored in the DB, it is possible to perform calculation at higher speed. In addition, by making the phase difference obtained by rigorous calculation using a three-dimensional structure mask under various lithography conditions into a function, the phase difference can be given as a function, and an optical image can be obtained at higher speed than DB access. It can also be requested.

  Although it is almost the same as DB, the phase difference between the 0th-order diffracted light and the 1st-order diffracted light is displayed as a distribution on a map in which the pupil of the projection optical system is divided into grids, that is, visually recognized by mapping on the pupil. It is also possible to improve the performance and simplify the simulation.

(Modification)
In addition, this invention is not limited to embodiment mentioned above. In the embodiment, the example of the pattern dimension design for the contact hole is shown, but other patterns (LS, isolated line, isolated space, isolated hole, LS periodic end) can be performed in a similar manner in a short time. Can be designed.

  Regarding the calculation of the non-periodic pattern, as shown in the flowchart of FIG. 12, after setting the illumination condition, mask condition, pattern type, pattern pitch, pattern dimension, light incident angle, etc. as initial values (step S71), The pattern M in the calculation area is divided into simple parts M1, M2, M3,... (Step S72), a shadow model is applied to each part to set a virtual mask, and the diffracted light amplitude is calculated (step S73). . Here, for the diffracted light amplitude by each part, the phase is called from the database (step S74), and the phase of the first-order diffracted light is newly calculated based on the called phase difference (step S75). Then, the optical images obtained from the parts are merged to obtain an optical image of the first pattern M (step S77).

  Further, the present invention is not limited to the processing for the phase of the first-order diffracted light. For example, even when the pattern size of interest is large and the diffracted light order entering the pupil is larger than 1, the phase difference corresponding to the diffracted light of that order Should be prepared.

  In addition, even when a plurality of patterns are on the same mask, the above method can be applied at the same time so that all the patterns on the mask are transferred onto the wafer within a desired size range. Needless to say, you can.

  In addition, the phase difference between the 0th-order diffracted light and the 1st-order diffracted light is obtained several times using the interval on the pupil as a variable, and when the necessary condition is an intermediate condition, interpolation is performed to obtain the phase difference distribution. Can be obtained approximately and used.

  In addition, various modifications can be made without departing from the scope of the present invention.

1 is a schematic block diagram showing an example of a projection exposure apparatus used in the present invention. The figure which shows the example which defined the mask of a solid structure as a mask of a planar structure newly considering only the shadow effect by oblique incidence. The figure which shows the method of giving a fixed transmittance | permeability and a phase to the part (fringe) used as the shadow around an opening part, and calculating. The figure which shows HP dependence of the phase difference of the 0th-order diffracted light of a L / S pattern of 1: 1, and a 1st-order diffracted light. The figure which shows the phase difference of the 0th-order diffracted light and the 1st-order diffracted light in the pupil plane of a projection lens. The figure which shows 0th-1st phase difference (DELTA) phi in the position on the pupil of a projection lens. The figure which shows the contact hole pattern made into object in embodiment of this invention. The figure which shows the 4th illumination used in the embodiment. The flowchart for demonstrating operation | movement of the optical image calculation part in the embodiment. 5 is a flowchart showing a procedure for determining a mask design value using the simulation method of the embodiment. The figure which shows the optical image calculation result by the simulation method of the embodiment. The flowchart for demonstrating the operation | movement of the optical image calculation part with respect to the pattern which is for demonstrating the modification of this invention and is not a periodic.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Light source 12 ... Mask 13 ... Projection optical system 14 ... Wafer (substrate)
DESCRIPTION OF SYMBOLS 21 ... Three-dimensional structure mask 22 ... Light-shielding part 31 ... Planar structure mask 32 ... The part used as the shadow around an opening part (fringe)
41 ... Contact hole pattern 42 ... Light source

Claims (5)

A simulation method of irradiating illumination light obliquely with respect to a mask plane and transferring a pattern formed on the mask onto a substrate via a projection optical system,
Defined by the distance between the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system, the thickness of the shielding part formed on the mask, the optical axis direction of the irradiation light and the incident direction on the mask 0th-order diffracted light and first-order diffracted light determined by a relationship corresponding to at least one of the angle of the difference between the mask pattern size and the half-cycle size of the mask pattern when the mask pattern is a periodic pattern A step of setting a phase difference between and
Executing a simulation based on the set phase difference;
A simulation method comprising:   The simulation method according to claim 1, wherein the simulation is performed using a mask in which a mask portion through which the irradiation light is transmitted is not hindered by the shielding portion is set as a mask pattern.   The step of setting the phase difference between the 0th-order diffracted light and the 1st-order diffracted light includes the step of setting the pupil plane of the projection optical system when the pattern formed on the three-dimensional structure mask is transferred onto the substrate via the projection optical system Based on a function that reads or stores the relationship between the phase difference between the zero-order diffracted light and the first-order diffracted light and at least one of the distance, the thickness, the angle, and the bias amount. The simulation method according to claim 1, wherein the calculation is performed.   The simulation method according to claim 1, wherein the phase difference between the 0th-order diffracted light and the 1st-order diffracted light is displayed as a distribution on a map obtained by dividing the pupil of the projection optical system into grids. A program for executing a simulation of irradiating illumination light obliquely with respect to a mask plane and transferring a pattern formed on the mask onto a substrate via a projection optical system,
Defined by the distance between the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system, the thickness of the shielding part formed on the mask, the optical axis direction of the irradiation light and the incident direction on the mask 0th-order diffracted light and first-order diffracted light determined by a relationship corresponding to at least one of the angle of the difference between the mask pattern size and the half-cycle size of the mask pattern when the mask pattern is a periodic pattern Means for setting the phase difference between and
Means for executing a simulation based on the set phase difference;
A computer-readable program characterized by causing a computer to execute.

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